In this paper, we present a number of numerical results concerning the newly introduced class of Hamiltonian Boundary Value Methods (hereafter, HBVMs). Such methods are very suited for the numerical integration of Hamiltonian problems, since they are able to preserve, in the discrete solution, the exact value of polynomial Hamiltonians. In such a way, a numerical drift of the Hamiltonian, sometimes experienced when solving such problems, cannot occur.
Hamiltonian BVMs (HBVMs): a family of "drift-free" methods for integrating polynomial Hamiltonian problems / L.Brugnano; F.Iavernaro; D.Trigiante. - In: AIP CONFERENCE PROCEEDINGS. - ISSN 0094-243X. - STAMPA. - 1168:(2009), pp. 715-718. (Intervento presentato al convegno ICNAAM 2009 tenutosi a Rethymno, Crete (Greece) nel 18-22 September 2009) [10.1063/1.3241566].
Hamiltonian BVMs (HBVMs): a family of "drift-free" methods for integrating polynomial Hamiltonian problems
BRUGNANO, LUIGI;TRIGIANTE, DONATO
2009
Abstract
In this paper, we present a number of numerical results concerning the newly introduced class of Hamiltonian Boundary Value Methods (hereafter, HBVMs). Such methods are very suited for the numerical integration of Hamiltonian problems, since they are able to preserve, in the discrete solution, the exact value of polynomial Hamiltonians. In such a way, a numerical drift of the Hamiltonian, sometimes experienced when solving such problems, cannot occur.
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